Killing Horizons

TL;DR

This paper explores the behavior of quantum states in two-dimensional QED across different observers, revealing issues with state representations in Rindler space and discussing how quantum corrections can eliminate horizons, leading to fuzzball solutions.

Contribution

It demonstrates the mismatch of physical states between Minkowski and Rindler observers in 2D QED and shows how quantum corrections can resolve horizon-related issues, connecting to fuzzball solutions.

Findings

Tracing over Rindler states yields non-physical density matrices.

States exact under Minkowski BRST are not necessarily BRST-closed in Rindler space.

Quantum corrections can eliminate horizons, leading to fuzzball solutions.

Abstract

QED in two-dimensional Minkowski space contains a single physical state as seen by an inertial observer or by a constantly accelerating Rindler observer. However in Feynman gauge if one takes a generic representative of the physical Minkowski state and traces over all left Rindler states, one does not arrive at a physical right Rindler state, but rather at a "density matrix" with negative eigenvalues for negative norm states corresponding intuitively to the radiation of uncorrelated temporal photons and ghosts. This reflects the fact that states that are exact under the Minkowski BRST operator are not necessarily exact or even closed under the Rindler BRST operator. Such situations are avoided when there are quantum corrections to the Hamiltonian that eliminate the horizons, which yield Mathurian fuzzball solutions.